Find the value of the constant c such that the vector field $\mathrm { G } ( x , y , x ) = \left( 5 x + 9 y ^ { 5 } + 3 z \right) \mathbf { i } + \left( 6 x ^ { 3 } + 2 y + 8 z \right) \mathbf { j } + ( c z - x ) \mathbf { k }$ is the curl of some vector field F.
A) -7
B) 0
C) 12
D) 3

Question

Quizplus · Accepted Answer

For a vector field G to be the curl of another vector field F, it must satisfy the condition that its divergence is zero. Calculating the divergence of G and setting it to zero gives the equation for c, which results in c = -7.

Find the Value of the Constant C Such That the Vector